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MA1001 - MATHEMATICS – I SYLLABUS
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MA1001 - MATHEMATICS – I
Module I: Preliminary Calculus & Infinite Series (9L + 3T)
Preliminary Calculus : Partial differentiation, Total differential and total derivative,
Exact differentials, Chain rule, Change of variables, Minima and Maxima of functions of two or
more variables.
Infinite Series : Notion of convergence and divergence of infinite series, Ratio test, Comparison
test, Raabe’s test, Root test, Series of positive and negative terms, Idea of absolute convergence,
Taylor’s and Maclaurin’s series.
Module II: Differential Equations (13L + 4T)
First order ordinary differential equations: Methods of solution, Existence and uniqueness of
solution, Orthogonal Trajectories, Applications of first order differential equations.
Linear second order equations: Homogeneous linear equations with constant coefficients,
fundamental system of solutions, Existence and uniqueness conditions, Wronskian, Non
homogeneous equations, Methods of Solutions, Applications.
Module III: Fourier Analysis (10 L+ 3T)
Periodic functions : Fourier series, Functions of arbitrary period, Even and odd functions, Half
Range Expansions, Harmonic analysis, Complex Fourier Series, Fourier Integrals, Fourier
Cosine and Sine Transforms, Fourier Transforms.
Module IV: Laplace Transforms (11L + 3T)
Gamma functions and Beta functions, Definition and Properties. Laplace Transforms, Inverse
Laplace Transforms, shifting Theorem, Transforms of derivatives and integrals, Solution of
differential Equations, Differentiation and Integration of Transforms, Convolution, Unit step
function, Second shifting Theorem, Laplace Transform of Periodic functions.
MA1002 - MATHEMATICS II
Module I (11 L + 3T)
Linear Algebra I: Systems of Linear Equations, Gauss’ elimination, Rank of a matrix,
Linear independence, Solutions of linear systems: existence, uniqueness, general form.
Vector spaces, Subspaces, Basis and Dimension, Inner product spaces, Gram-Schmidt
orthogonalization, Linear Transformations.
Module II (11 L+ 3T)
Linear Algebra II: Eigen values and Eigen vectors of a matrix, Some applications of Eigen
value problems, Cayley-Hamilton Theorem, Quadratic forms, Complex matrices, Similarity of
matrices, Basis of Eigen vectors – Diagonalization.
Module III (10L+3T)
Vector Calculus I: Vector and Scalar functions and fields, Derivatives, Curves, Tangents,
Arc length, Curvature, Gradient of a Scalar Field, Directional derivative, Divergence of a vector
field, Curl of a Vector field.
Module IV (11 L+4T)
Vector Calculus II: Line Integrals, Line Integrals independent of path, Double integrals,
Surface integrals, Triple Integrals, Verification and simple applications of Green’s Theorem,
Gauss’ Divergence Theorem and Stoke’s Theorem.